Abstract: We establish a connection between the hyperbolic relativistic Calogero-Mosersystems and a class of soliton solutions to the Tzitzeica equation aka theDodd-Bullough-Zhiber-Shabat-Mikhailov equation. In the 6N-dimensional phasespace $\Omega$ of the relativistic systems with 2N particles and $N$antiparticles, there exists a 2N-dimensional Poincar\-e-invariant submanifold$\Omega P$ corresponding to $N$ free particles and $N$ boundparticle-antiparticle pairs in their ground state. The Tzitzeica $N$-solitontau-functions under consideration are real-valued, and obtained via the dualLax matrix evaluated in points of $\Omega P$. This correspondence leads to apicture of the soliton as a cluster of two particles and one antiparticle intheir lowest internal energy state.